These Dl+1 values are treated as previously described for the 

 manually digitized data for which Dl=20. All this is done internally 

 in the computer and the output is the amplitude of the first harmonic 

 motion at consecutive measurement stations. A search routine was also 

 included in the computer program so that the maximum and minimum values 

 of the wave amplitude were determined and the resulting estimates of the 

 reflection coefficient were printed out for each experimental run. 

 Although the computerized procedure was thoroughly checked against the 

 manual procedure before the former was adopted for the experiments 

 listed in Appendix B, Tables B-1 and B-3, the procedure of obtaining a 

 paper tape wave record was continued to avoid possible loss of 

 experimental data. 



An example of the added accuracy involved when a more exact method 

 is inacted is seen by examining the example described in Section lll.S.b, 

 Figure 20. From Figure 20, as previously noted, the raw data from the 

 ejcperiment (the open circles] do not reproduce a well-behaved wave ampli- 

 tude variation. Through the use of the Fourier series computer program, 

 the raw data were corrected, i.e., only the first-order wave amplitude 

 was retained, and the corrected data are seen in Figure 20 as the solid 

 circles. It is observed from studying the corrected data that the 

 minimum amplitude locations are not precise and one must fit a theoretical 

 curve to the corrected data to determine the minimum wave amplitude and 

 the resulting reflection coefficient. The theoretical curve with R=0.88 

 appears to fit the data presented in Figure 20 well, but as it will be 

 demonstrated, the wave amplitudes immediately surrounding a minimum have 

 to be determined at a much closer spacing than used in the experiments 

 presented in Figure 20 if the curve-fitting procedure is to be eliminated. 



Figure C-1 is a graphical representation of equation (123) close to 

 a node location for various reflection coefficients. It is clearly seen 

 that, as the spacing between measurements becomes larger, one is able to 

 have relatively large errors in obtaining the minimum location especially 

 for high reflection coefficients. For example, a 4-inch (10 centimeters) 

 spacing corresponds to a measurement interval, Ax/L, of 0.03 for the 2- 

 second wave in the present experiment. The maximum deviation would occur 

 when the measurement locations were equally spaced around the minimum, 

 i.e., Ax/L equal to 0.015 on either side of the minimum. If one had an 

 actual reflection coefficient of R=0.88 one would obtain a value of 

 ^/^ax 6<^ual to 0.115 for a maximum displacement from the actual minimum. 

 Therefore, if one assumed that the reading of a-fa-x^ax ~ 0.115 was the 

 correct minimum value, then the reflection coefficient would be determined 

 from Figure C-1 R=0.79 which is approximately a 10-percent error. 

 Similarly, if one has an actual reflection coefficient of R=0.60 and 

 collected data at the maximum deviation locations, the error incurred 

 would only be of the order 3 percent. It is apparent that the errorsrors 

 are most prevalent when one has high reflection coefficients. The 

 computer program described previously allows one to collect a large number 

 of data points and analyze them quickly so that the measurement interval 

 can be reduced in the vicinity of nodes, thus resulting in smaller errors. 



